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Loop quantization of a weak-coupling limit of Euclidean gravity

I will describe recent work in collaboration with Adam
Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a
certain $G_{\mathrm{N}}\rightarrow 0$ limit of Euclidean gravity, introduced by
Smolin. The model allows one to test various quantization choices one is faced
with in loop quantum gravity, but in a simplified setting. The main results are the construction of
finite-triangulation Hamiltonian and diffeomorphism constraint operators whose
continuum limits can be evaluated in a precise sense, such that the quantum
Dirac algebra of constraints closes nontrivially and free of anomalies. The construction relies heavily on techniques
of Thiemann's QSD treatment, and lessons learned applying such techniques to
the loop quantization of parameterized scalar field theory and the
diffeomorphism constraint in loop quantum gravity. I will also briefly discuss the status of the
quantum constraint algebra in full LQG, and how some of the lessons learned from
the present model may guide us in that setting.